Hartwig symbols
نویسندگان
چکیده
منابع مشابه
The Extended Fisher-hartwig Conjecture for Symbols with Multiple Jump Discontinuities
The asymptotic expansions of Toeplitz determinants of certain symbols with multiple jump discontinuities are shown to satisfy a revised version of the conjecture of Fisher and Hartwig. The Toeplitz matrix T n [φ] is said to be generated by the function φ if T n [φ] = (φ i−j), i, j = 0,. .. , n − 1. where φ n = 1 2π 2π 0 φ(θ)e −inθ dθ is the nth Fourier coefficient of φ. Define the determinant T...
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The paper is devoted to exact and asymptotic formulas for the determinants of Toeplitz matrices with perturbations by blocks of fixed size in the four corners. If the norms of the inverses of the unperturbed matrices remain bounded as the matrix dimension goes to infinity, then standard perturbation theory yields asymptotic expressions for the perturbed determinants. This premise is not satisfi...
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We describe the asymptotics of the spectral norm of finite Toeplitz matrices generated by functions with Fisher-Hartwig singularities as the matrix dimension goes to infinity. In the case of positive generating functions, our result provides the asymptotics of the largest eigenvalue, which is of interest in time series with long-range memory.
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With localization techniques one can obtain general limit theorems for Toeplitz determinants with Fisher-Hartwig singularities from the asymptotics for any symbol with one singularity of general type. There exists a family of these for which the determinants can be evaluated explicitly and their asymptotics determined. But for the Wiener-Hopf analogue, although there are likely analogous locali...
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